Dean entered his sister into their town's Smelly Shoe Competition. Dean observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes. What is the probability that a randomly selected contestant is not 31 to 50 years old and is not wearing tennis shoes?Simplify any fractions.

Question

Tennis Shoes High Heels
Under age 12 4 2
13 to 30 years old 7 7
31 to 50 years old 6 6
17/32
15/16
13/32
9/32

Answer 1

First, let's find the total number of contestants who are not 31 to 50 years old and are not wearing tennis shoes:

- Under age 12: 2 (High Heels)
- 13 to 30 years old: 7 (Tennis Shoes) + 7 (High Heels) = 14
- 31 to 50 years old: We want to exclude this category, which contains 6 (Tennis Shoes) + 6 (High Heels) = 12 contestants

Therefore, the total number of contestants who are not 31 to 50 years old and are not wearing tennis shoes is 2 + 14 = 16.

Now, the total number of contestants is:
- Under age 12: 4 (Tennis Shoes) + 2 (High Heels) = 6
- 13 to 30 years old: 7 (Tennis Shoes) + 7 (High Heels) = 14
- 31 to 50 years old: 6 (Tennis Shoes) + 6 (High Heels) = 12

The total number of contestants is 6 + 14 + 12 = 32.

The probability that a randomly selected contestant is not 31 to 50 years old and is not wearing tennis shoes is 16/32 = 1/2.

So, the correct answer is 1/2, which can be simplified as 16/32 = 1/2.